How the Japan Earthquake Made the Day Shorter

The enormous tsunami-spawning earthquake off Japan Friday not only shifted the planet's axis by several inches, it also sped up the Earth's rotation, shortening each day by 1.8 microseconds. Richard Gross, man who calculates these changes at NASA's Jet Propulsion Lab, tells PM how he does it—and why those millionths of a second matter. (Hint: If JPL didn't account for it, Mars rovers would miss their targets.)

How do earthquakes change the Earth's rotational speed and axis?

Earthquakes can change the Earth's rotation by rearranging the Earth's mass. This is what a spinning ice skater does to make herself spin faster. She moves her arms closer to her bodyshe's moving her mass closer to the axis about which she's rotating. And earthquakes do the same thing. This earthquake must've moved the mass on average a bit closer to the Earth's rotation axis to make the Earth rotate faster and the length of the day a bit smaller.

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How do you figure out such tiny differences?

What I do is a calculation. I start with an initial model for how the mass is distributed everywhere within the Earth. And then I use seismic estimates for how the fault slipped during the earthquake, and I use those estimates to tell me how that initial mass distribution changed as a result of the earthquake.

The earthquake is basically a force that acts on the Earth, causing it to deform. I compute that deformation everywhere throughout the solid body of the Earth. Then, by conservation of angular momentum, if I know how the Earth's mass was rearranged, then I know how the Earth's rotation must've changed. Just like the ice skater.

The shift in the planet's axis and rotational speed that you've calculated for the Japan earthquake is different than for other huge quakes, like last year's in Chile and the 2004 Sumatran quake that spawned the enormous tsunami in South Asia. Why is that?

There are three factors that are important in this. One, of course is the size. If everything else is the same, then the larger the earthquake, the larger its impact on the Earth's rotation. Location is also important. If the earthquake occurs on the equator, then it's going to have a bigger effect than if it occurs at the north or south poles. If you move mass up or down at the north or south pole, it has no effect on the spin of the Earth at all. And then, the details of how the fault slipped during the earthquakethe dip angle of the fault and in what direction the slip occurredis also important. Vertical motion is much more effective in changing the length of the day than horizontal motion that you get in a strike-slip fault. A thrust fault like [what caused] the Japanese earthquake has vertical motion; it is more effective in changing the length of the day than, say, an earthquake we'd get on the San Andreas here in California.

Have you already done your own calculations for the Japanese earthquake's effects?

The earlier calculations were done by an Italian group. My calculations are a bit differenttheir latest calculation is 25 centimeters for the shift in the figure axis [the axis about which the Earth's mass is balanced], and my calculation is like 17 cm. We're a bit different, but in the same ballpark.

Seventeen centimeters is still quite a bit more than a few of the previous quakes: You calculated 7 cm in the planet's axis shift for the 2004 9.1 Sumatran earthquake, and about 8 cm for Chile's 8.8 magnitude quake last year.

That's right. This one is really about twice as big. Those other changes were too small to be observed, but this one we might be able to see in our data because it's about three times as big as the error in making the measurements of the position of the figure axis. But there is a complicating factor in doing that: The figure axis changes all the time. Anything that rearranges the Earth's mass changes the position of the figure axis. And the biggest changes are in fact due to the circulation of the atmosphere and the ocean. They're in constant motion, so the figure axis is constantly responding to that. So over the course of a year, the figure axis can change by about a meterabout six times bigger than what we're seeing caused by this earthquake.

So, in order to see this earthquake in our data, we have to be able to remove these larger effects of the atmosphere and oceans. How well we can do that will determine whether we can actually see this.

How do you make those measurements, exactly?

We actually use GPS. We have a worldwide network of GPS receivers that tells us how the Earth is oriented with respect to a constellation of GPS satellites. Over time, we see changes to that orientation or changes in the Earth's rotation.

These changes may be too small to notice on an everyday basis, but what are the scientific consequences of these shifts in the Earth's axis?

For the most part, there are no practical consequences of thismost people don't notice these changes. But we worry about it here at JPL because it does affect our ability to navigate spacecraft to distant objects like Mars. If we want to be able to land a rover on the surface of Mars exactly where we want, a pinpoint landing, to do that precise navigation we have to account for these small changes in the Earth's rotation. If we didn't account for themif we assumed that the Earth was just rotating uniformlythen we might miss Mars entirely when we send a spacecraft.

So it's a tiny change here, but when you extrapolate to the distance from here to Marsthat's where you see the effect?

Exactly. These changes in rotation are angular measures. On the surface of the Earth it's a small amount, but by the time you get to the distance of Mars it can be big. It can be kilometers of difference in the accuracy of landing a rover.